(it works!) Neural Network, Self Organizing Map, and Mandelbrot Set

[ker2x]

Why ? Because i can \o/

It's still an early preview, too much copy/paste from GPL code.
But i promise to release the source as GPL really soon

About SOM : http://en.wikipedia.org/wiki/Self-organizing_map

[ker2x]

the code to generate the mandelbrot set edge :

Code:

            double zr, zi, cr, ci, temp = 0.0;
            int i = 0;

            while (i < mandelbrotPoints)
            {
                int iter = 0;
                zr = 0.0;
                zi = 0.0;
                cr = randomGenerator.NextDouble() * 4 - 2.0f;
                ci = randomGenerator.NextDouble() * 4 - 2.0f;
                int intermediaire = 50;

                while ((iter < intermediaire) && ((zr * zr + zi * zi) < mandelbrotEscapeRadius))
                {
                    temp = zr * zi;
                    zr = zr * zr - zi * zi + cr;
                    zi = temp + temp + ci;
                    iter++;
                }
                if ((iter == intermediaire))   //if in MSET at intermediaire value
                {

                    while ((iter < mandelbrotMaxIteration) && ((zr * zr + zi * zi) < mandelbrotEscapeRadius))
                    {
                        temp = zr * zi;
                        zr = zr * zr - zi * zi + cr;
                        zi = temp + temp + ci;
                        iter++;
                    }
                    if ((iter < mandelbrotMaxIteration))   //If exited at max (then if at the border)
                    {
                        trainingSet.Add(new TrainingSample(new double[] { (cr + 2.0) * 25.0, (ci + 2.0) * 25.0 }));
                        lineItem.AddPoint((cr + 2.0) * 25.0, (ci + 2.0) * 25.0);
                        i++;
                    }

                }


            }

Probably not optimal but very simple.
Explanation :

- if at 50 iteration it escaped, it's not in the mandelbrot set and i skip the point.
- if at 50 iteration it hasn't escaped it's in the mandelbrot set
- then i continue up to 100 iteration and check if it escaped.
- if the point hasn't escaped at 50 and hasn't escaped at 100, it may be anywhere inside the mandelbrot set so i skip this point.
- if the point hasn't escaped at 50 but escaped at 100, then it's on the edge so i keep the point

[The Rev]

I have no idea what you're talking about, but it sounds really cool.

The Rev

[ker2x]

I have no idea what you're talking about, but it sounds really cool.

LOL !!! 
I guess it deserve some explanation, i'll try to explain later. i'm at work and too busy to write a good explanation

I can answer to the most obvious question :
- Is it usefull ? Probably not.
- What's the goal ? How can i use this in my fractal software ? No idea! I just tought it was a cool thing to do...

[The Rev]

If it is inspiring, then it's definitely useful!

The Rev

[ker2x]

The network on the right try to organize itself to imitate the training set on the left.
...
Flawless victory \o/

[ker2x]

Here is the binary (windows executable "Any CPU") : http://fractals.s3.amazonaws.com/app/mandelbrotSOM.zip
Here is the binary + src (Visual Studio 2008 project) : http://fractals.s3.amazonaws.com/app/mandelbrotSOM_src-included.zip

Beware, the source is a mayhem :
- it's a modified sample application from the NeuroDotNet, i will clean that.
- I don't know how to correctly distribute VisualStudio Project. It may work, or not... but the sources are definitively included.

It's GPL code since the original sample app is GPL too.

There is a few bug or missing feature (eg : it doesn't check if MinIter < MaxIter)

Howto :
- Launch the executable, clic start. The network on the right will try to organize itself to look like the training set on the left
- Change nb of plots from 500 to 1000. Click on "generate mandelbrot set". The training set will have more points (more complete). Feel free to clic start.
- Change Layer Width and Layer Height from 12 to 20. The networks on the right will have more node. Click start. It will be slower.
- Uncheck Show Connections. it will not display the edge between node. computation will be faster.
- Check Show only Winner. it will not display the node that are not close to the training set. it will be faster too.
- now the map will look like the training set. (see picture in previous post).

- You can eventually change min iteration to 500, and max iteration to 1000. Click on generate mandelbrot set (it may take some time and the app will hang while computing the training set). The training set will be finer.

Feel free to play with other options.
If you play with layer shape, topology or neighborood function, you should enable show connection and disable show only winner to understand what it does.
If you play with learning rate and training cycle, i suggest to learn about neural network and Self organizing map

Enjoy ! Feel free to report bug, or post suggestion.

[ker2x]

you will find some documentation about SOM and NeuroDotNet (the library used for this app), here : http://neurondotnet.freehostia.com/manual/index.html

[ker2x]

if you want to see "smoother" map transformation, change your Learning rate to 0.0001

[cbuchner1]

now what's the use of such neural net, once it is trained?

Could it be used to recognize patterns - such as finding minibulbs in the M-set?

Christian

[ker2x]

now what's the use of such neural net, once it is trained?

dunno.

Could it be used to recognize patterns - such as finding minibulbs in the M-set?

It could probably be done with a (multilayer) perceptron. ( http://en.wikipedia.org/wiki/Perceptron )

[Tglad]

I don't see how any feed-forward neural net could do any better than the polynomial lemniscates that are already a well defined approximation
http://mathworld.wolfram.com/MandelbrotSetLemniscate.html
A recurrent neural net might be capable of something cleverer.

[ker2x]

I don't see how any feed-forward neural net could do any better than the polynomial lemniscates that are already a well defined approximation
http://mathworld.wolfram.com/MandelbrotSetLemniscate.html
A recurrent neural net might be capable of something cleverer.

You're right. totally right